IJPAM: Volume 26, No. 4 (2006)

$l^q$-VALUED EXTENSION OF THE FRACTIONAL
MAXIMAL OPERATORS FOR NON-DOUBLING MEASURES
VIA POTENTIAL OPERATORS

Yoshihiro Sawano
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, JAPAN
e-mail: yosihiro@ms.u-tokyo.ac.jp


Abstract.In this paper we consider fractional maximal operators with Radon measure on $\R^d$. We do not pose any assumption on the measure $\mu$ except that the measure is non-zero. For the proof we construct Riesz-like potential operators for $\mu$.

Received: December 5, 2005

AMS Subject Classification: 26A33

Key Words and Phrases: operators for integration and differentiation of fractional order

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 4